The acceleration - displacement graph of a particle moving in a straight line is given as in the figure . The initial velocity of the particle is zero. Find the velocity of the particle when displacement of the particle is `s=12m`.

Explanation

From the equation `v^(2)-u^(2)=2as`
as`=(v^(2)-u^(2))/2=`area under a-s graph
initial velocity `u=0,`
`:.`as `=v^(2)/2=` area under a-s graph.
`:. V=sqrt(2("areaunder a-s graph"))`
`=sqrt[1/2(2)(2)+6xx2+1/2(2+4)2+1/2(2)4]2=sqrt(2xx24)=4sqrt3ms^(-1)`